Reduced complexity detector for multiple-antenna systems

ABSTRACT

A reduced-complexity maximum-likelihood detector that provides a high degree of signal detection accuracy while maintaining high processing speeds. A communication system implementing the present invention comprises a plurality of transmit sources operable to transmit a plurality of symbols over a plurality of channels, wherein the detector is operable to receive symbols corresponding to the transmitted symbols. The detector processes the received symbols to obtain initial estimates of the transmitted symbols and then uses the initial estimates to generate a plurality of reduced search sets. The reduced search sets are then used to generate decisions for detecting the transmitted symbols. In various embodiments of the invention, the decisions for detecting the symbols can be hard decisions or soft decisions. Furthermore, in various embodiments of the invention, the initial estimates can be obtained using a plurality of linear equalization techniques, including zero-forcing equalization, minimum-mean-squared-error equalization. The initial estimate can also be obtained by nulling and canceling techniques. In various embodiments of the invention, the data output corresponding to the transmitted symbols can be obtained using a log-likelihood probability ratio. The method and apparatus of the present invention can be applied to any communication system with multiple transmit streams.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is directed in general to wireless communicationsystems. In one aspect, the present invention relates to a method andsystem for improving the performance of wireless transceivers byproviding an improved detector for multiple-antenna systems.

2. Description of the Related Art

Modern communication systems support wireless and wire-linedcommunications between a wide variety of wireless and/or wire-linedcommunication devices. Such communication systems range from nationaland/or international cellular telephone systems to the Internet topoint-to-point in-home wireless networks. Each type of communicationsystem is constructed, and hence operates, in accordance with one ormore communication standards. For instance, wireless communicationsystems may operate in accordance with one or more standards including,but not limited to, IEEE 802.11, Bluetooth (BT), advanced mobile phoneservices (AMPS), digital AMPS, global system for mobile communications(GSM), code division multiple access (CDMA), local multi-pointdistribution systems (LMDS), multi-channel-multi-point distributionsystems (MMDS) and/or variations thereof.

Depending on the type of wireless communication system, a wirelesscommunication device (such as a cellular telephone, two-way radio,personal digital assistant (PDA), personal computer (PC), laptopcomputer, home entertainment equipment, etc.) communicates directly orindirectly with other wireless communication devices. For directcommunications (also known as point-to-point communications), theparticipating wireless communication devices tune their receivers andtransmitters to the same channel or channels (e.g., one of the pluralityof radio frequency (RF) carriers of the wireless communication system)and communicate over the tuned channel(s). For indirect wirelesscommunications, each wireless communication device communicates directlywith an associated base station (e.g., for cellular services) and/or anassociated access point (e.g., for an in-home or in-building wirelessnetwork) via an assigned channel. To complete a communication connectionbetween the wireless communication devices, the associated base stationsand/or associated access points communicate with each other directly,via a system controller, via the public switched telephone network, viathe Internet, and/or via some other wide area network.

Wireless communication devices typically communicate with one anotherusing a radio transceiver (i.e., receiver and transmitter) that may beincorporated in, or coupled to, the wireless communication device. Thetransmitter typically includes a data modulation stage, one or moreintermediate frequency stages and a power amplifier. The data modulationstage converts raw data into baseband signals in accordance with aparticular wireless communication standard. The intermediate frequencystages mix the baseband signals with one or more local oscillations toproduce RF signals. The power amplifier amplifies the RF signals priorto transmission via an antenna.

The receiver is typically coupled to an antenna and includes a low noiseamplifier, one or more intermediate frequency stages, a filtering stageand a data recovery stage. The low noise amplifier receives inbound RFsignals via the antenna and amplifies them. The intermediate frequencystages mix the amplified RF signals with one or more local oscillationsto convert the amplified RF signal into baseband signals or intermediatefrequency (IF) signals. The filtering stage filters the baseband signalsor the IF signals to attenuate unwanted out of band signals to producefiltered signals. The data recovery stage recovers raw data from thefiltered signals in accordance with the particular wirelesscommunication standard.

In wireless communication systems utilizing the various 802.11standards, the allowable bandwidth is set by standard-settingassociations and governmental agencies. To achieve higher datathroughput, many later generation wireless systems, such as those basedon the 802.11n standard use Multiple Input Multiple Output (MIMO)antenna systems. MIMO systems use multiple transmit antennas to transmitmultiple data streams in the same frequency spectrum and take advantageof multipath channels with a plurality of receive antennas being used torecover the information transmitted over the various data streams. Thusin a MIMO system, information is transmitted and received simultaneouslyusing multiple transmit and receive antennas. In such a system, eachpair of transmit and receive antennas defines a signal path from thetransmitter to the receiver.

MIMO technology has been adopted by the Institute for Electrical andElectronic Engineers (IEEE) for the next generation wireless local areanetwork (WLAN) to provide a throughput of at least one hundred Mbps.Transmission protocols and standards for such a high throughput (WLAN)are embodied in a standard referred to as 802.11n. Since 802.11n is aMIMO extension of current WLAN standards, such as 802.11a and 802.11g,802.11n will also be based on the transmission scheme referred to asorthogonal frequency division multiplexing (OFDM).

A MIMO system can provide two types of gain: (1) diversity gain, and (2)spatial multiplexing gain. Diversity gain is realized when signalscarrying the first information are sent via different paths. Thismultipath transmission increases the robustness of transmission or thereliability of reception. Spatial multiplexing gain is realized whensignals carrying independent information are sent in parallel viadifferent paths. This increases the length throughput or the data rateof the wireless communication system.

In MIMO systems, there is a need to obtain an estimate of thetransmitted signal with a high degree of accuracy. However, there is aninherent tradeoff between maximum accuracy and the speed of processingthe signal. The optimum detector is a maximum-likelihood detector. Giventhe received symbol vector y, the maximum-likelihood detector searchesover all possible transmitted symbol vectors x_(j) for the transmitvector that maximizes the conditional probability Pr{x_(j)/y}, therebyminimizing the probability of decoding error at the receiver. This besttransmit symbol vector represents a hard decision. Since communicationsystems will employ some form of coding, to improve performance further,the output of the maximum-likelihood detector should be a measure ofreliability of each transmitted bit. These reliabilities are also knownas soft decisions. However, the maximum-likelihood detector involvessearching over all the possible combinations of transmit symbols. For asystem with multiple transmit antennas, the complexity growsexponentially with the number of transmit antennas. Hence,reduced-complexity schemes that still give comparable performance to theoptimum maximum-likelihood detector is necessary.

SUMMARY OF THE INVENTION

The method and apparatus of the present invention provides areduced-complexity maximum-likelihood detector that provides a highdegree of signal detection accuracy while maintaining high processingspeeds. The reduced-complexity maximum-likelihood detector of thepresent invention uses a reduced search set of all possible transmitsymbols. As will be understood by those of skill in the art, limitingthe search set too much can result in poor detection, thereby degradingsystem performance. However, a search set that is too large can resultin increased latency. The method and apparatus of the present inventionuses estimation schemes to estimate the nucleus of an optimum searchset. In various embodiments of the invention different schemes,discussed hereinbelow, are used to estimate the transmit symbols and tofind the search set around the estimated transmit symbols. The methodand apparatus of the present invention can be applied to anycommunication system with multiple transmit streams.

In one embodiment of the invention, a communication system implementingthe present invention comprises a plurality of transmit sources operableto transmit a plurality of symbols over a plurality of channels, whereinthe detector is operable to receive symbols corresponding to saidtransmitted symbols. The detector processes the received symbols toobtain initial estimates of said transmitted symbols and then uses theinitial estimates to generate a plurality of reduced search sets. Thereduced search sets are then used to generate decisions for detectingsaid transmitted symbols. In various embodiments of the invention, thedecisions for detecting the symbols can be hard decisions or softdecisions. Furthermore, in various embodiments of the invention, theinitial estimates can be obtained using a plurality of linearequalization techniques, including zero-forcing equalization,minimum-mean-squared-error equalization. The initial estimate can alsobe obtained by nulling and canceling techniques. In various embodimentsof the invention, the data output corresponding to the transmittedsymbols can be obtained using a log-likelihood probability ratio.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be better understood, and its numerousobjects, features and advantages made apparent to those skilled in theart by referencing the accompanying drawings. The use of the samereference number throughout the several figures designates a like orsimilar element.

FIG. 1 is an illustration of the generalized functional components forimplementing a MIMO system with a plurality of transmit antennas and aplurality of receive antennas.

FIG. 2 is an illustration of the generalized functional components forimplementing a MIMO system with two transmit antennas and two receiveantennas for a system using orthogonal frequency division multiplexing.

FIG. 3A is a block diagram illustration of the functional components ofa MIMO detector in accordance with one embodiment of the presentinvention wherein the detector generates a “soft” decision.

FIG. 3B is a block diagram illustration of the functional components ofa MIMO detector in accordance with one embodiment of the presentinvention wherein the detector generates an estimate used to make a harddecision.

FIG. 4 is an illustration of a 4-QAM constellation of symbols processedby the MIMO detector of FIG. 1.

FIG. 5 is an illustration of a constellation of symbols processed by theMIMO detector of FIG. 1 by equalizing the received vector to producenoisy estimates and slicing the noisy estimates to nearest constellationpoints.

FIG. 6 is an illustration of a 2×2 16 QAM constellation of symbolsprocessed by the MIMO detector of FIG. 1 to obtain a reduced set ofpossible transmit symbol vectors.

FIG. 7 is an illustration of the 2×2 16 QAM constellation of symbols ofFIG. 4 further processed by a first method to complete the LLRcalculation for each bit.

FIG. 8 is an illustration of a 2×2 16 QAM constellation of symbols ofFIG. 4 further processed by a second method to complete the LLRcalculation for each bit.

DETAILED DESCRIPTION

A method and apparatus for an improved wireless communication system isdescribed. While various details are set forth in the followingdescription, it will be appreciated that the present invention may bepracticed without these specific details. For example, selected aspectsare shown in block diagram form, rather than in detail, in order toavoid obscuring the present invention. Some portions of the detaileddescriptions provided herein are presented in terms of algorithms oroperations on data within a computer memory. Such descriptions andrepresentations are used by those skilled in the field of communicationsystems to describe and convey the substance of their work to othersskilled in the art. In general, an algorithm refers to a self-consistentsequence of steps leading to a desired result, where a “step” refers toa manipulation of physical quantities which may, though need notnecessarily, take the form of electrical or magnetic signals capable ofbeing stored, transferred, combined, compared, and otherwisemanipulated. It is common usage to refer to these signals as bits,values, elements, symbols, characters, terms, numbers, or the like.These and similar terms may be associated with the appropriate physicalquantities and are merely convenient labels applied to these quantities.Unless specifically stated otherwise as apparent from the followingdiscussion, it is appreciated that throughout the description,discussions using terms such as processing, computing, calculating,determining, displaying or the like, refer to the action and processesof a computer system, or similar electronic computing device, thatmanipulates and/or transforms data represented as physical, electronicand/or magnetic quantities within the computer system's registers andmemories into other data similarly represented as physical quantitieswithin the computer system memories or registers or other suchinformation storage, transmission or display devices.

FIG. 1 is an illustration of the functional components of a generalizedcommunication system 100 for implementing a MIMO system with twotransmit antennas and two receive antennas. A bit stream is received byencoder 102 which generates an encoded input for the vector modulator104. A plurality of antennas 106 and 108 are operable to communicateover a plurality of communication channels 110, thereby defining aplurality of MIMO communication channels. As will be understood by thoseof skill in the art, the data received by antennas 108 will containnoise. The MIMO detection module 112 is operable to process the incomingdata to provide “soft” or “hard” decisions regarding the received data.These “soft” or “hard” decisions are used by the detector 114 togenerate an accurate output bit stream that avoids corruption related tothe effects of noise.

FIG. 2 is an illustration of the functional components of acommunication system 200 for implementing MIMO communications using OFDMwith two transmit antennas and two receive antennas. The illustration inFIG. 2 is operable to binary input data using a MIMO protocol for aWLAN. The MIMO system 200 in FIG. 2 comprises an encoder 202 and aninterleaver 204. The output from the interleaver 204 is separated intofirst and second data streams that are provided to QAM mapping modules206 and 208. The QAM mapping modules 206 and 208 provide quadratureamplitude modulated data streams that are provided to inverse fastFourier transform (IFFT) add guard interval modules 210 and 212,respectively. The IFFT add guard interval modules 210 and 212 transmitmodulated data streams via antennas 214 and 216. As will be understoodby those of skill in the art, the data transmitted by antennas 214 and216 can be propagated by MIMO multipath channels 218 between the varioustransmit and receive antennas. The signals received by antennas 220 and222 are processed by strip guard interval fast Fourier transform (FFT)modules 224 and 226, that generate inputs to the MIMO detection module228. The processed signals from the strip guard interval FFT modules areprocessed by the MIMO detection module 228 which then provides “soft” or“hard” decisions to the decoder 230 to generate a binary output datastream.

FIG. 3 a is an illustration of the functional components of a MIMO softdetector 112 a in accordance with the present invention for generatingsoft decisions for data streams comprising noisy signals. The incomingdata is processed in three stages. In the first stage 302, the noisyreceived symbols are processed by an equalization-based detector togenerate initial estimates of the transmitted symbols using techniquesdiscussed in greater detail below. In the second stage 304, the initialestimates are processed to form a reduced search set based onpredetermined criteria discussed below. In the third stage 306, LLRcomputation is performed over the reduced search to generate softdecisions for use by the decoder 114.

FIG. 3 b is an illustration of the functional components of a MIMO harddetector 112 b in accordance with the present invention for generatinghard decisions for data streams comprising noisy signals. The incomingdata is processed in three stages. In the first stage 302, the noisyreceived symbols are processed by an equalization-based detector togenerate initial estimates of the transmitted symbols using techniquesdiscussed in greater detail below. In the second stage 304, the initialestimates are processed to form a reduced search set based onpredetermined criteria discussed below. In the third stage 308, the bestestimate of the transmit symbols is found over the reduced search set.From this best estimate hard decisions are generated for use by thedecoder 114. Since the corresponding bit mapping is known, the decoderreceives bits rather than probabilistic data.

As will be understood by those of skill in the art, a MIMO soft decoderestimates the reliability of each possible decision regarding a receivedsymbol without making an actual decision regarding the symbol. Thedecoder uses the estimated reliabilities, or soft decisions, provided bythe MIMO soft detector to decode the received symbols, therebygenerating a decoded binary output data stream.

The method and apparatus of the present invention can be understood byconsidering the processing of received signals by the MIMO detectionmodule 112 in a generalized communication system such as thatillustrated in FIG. 1 with N_(t) transmit antennas and N_(r) receiveantennas. If the channel is a narrowband flat-fading channel or if OFDMmodulation format is used, this N_(t)×N_(r) system can be described bythe following model: $\begin{matrix}{\begin{bmatrix}{y_{1}(n)} \\{y_{2}(n)} \\\vdots \\{y_{Nr}(n)}\end{bmatrix} = {{\begin{bmatrix}{H_{11}(n)} & {H_{12}(n)} & \cdots & {H_{1{Nt}}(n)} \\{H_{21}(n)} & {H_{22}(n)} & \cdots & {H_{2{Nt}}(n)} \\\vdots & \vdots & ⋰ & \vdots \\{H_{{Nr}\quad 1}(n)} & {H_{{Nr}\quad 2}(n)} & \cdots & {H_{NrNt}(n)}\end{bmatrix}\begin{bmatrix}{x_{1}(n)} \\{x_{1}(n)} \\\vdots \\{x_{Nt}(n)}\end{bmatrix}} + \begin{bmatrix}{N_{1}(n)} \\{N_{1}(n)} \\\vdots \\{N_{Nt}(n)}\end{bmatrix}}} & {{Eq}\quad 1} \\{{y(n)} = {{{H(n)} \times (n)} + {N(n)}}} & {{Eq}\quad 2}\end{matrix}$Where: n is the time or frequency index

y is the N_(r)×1 receive vector

H is the N_(r)×N_(t) channel matrix

x is the N_(t)×1 transmit vector

N is the N_(r)×1 noise vector

Without loss of generality, the time/frequency index is dropped and themodel becomesy=Hx+N  Eq 3

In addition, it can be assumed that the channel matrix H is perfectlyknown at the receiver and that the noise samples N_(i) are independentcomplex Gaussian variables with zero mean and variance σ².

From Equation 1, the received signal at antenna j, y_(j), is a noisysuperposition of the N_(t) transmitted symbols, x_(i), that arecorrupted by the channel matrix H as described by the followingequation: $\begin{matrix}{{y_{j} = {{\sum\limits_{i = 1}^{N_{t}}{H_{ji}x_{i}}} + N_{j}}},\quad{j = 1},\ldots\quad,N_{r}} & {{Eq}\quad 4}\end{matrix}$

Each symbol x_(i) is mapped from log₂(M) bits where M is the size of theconstellation. For example, if x_(i) is drawn from a 4-QAMconstellation, then each x_(i) is mapped from 2 bits. In Equation 4, thetotal number of bits transmitted is N_(t)log₂(M) bits. This willhereinafter be denoted as a transmit bit vector [b₁ b₂ . . . b_(L)]where L=N_(t)log₂(M).

As discussed hereinabove, the soft-output maximum-likelihood detector228 is optimum because it minimizes the probability of incorrectdecisions. The soft-output maximum-likelihood detector 228 receives yand searches over all possible transmit symbol vectors x to produce softinformation about the likelihood of the transmitted bits b₁, 1=1, . . ., N_(t)log₂(M) being a 0 or a 1.

The soft information of each b₁=0 or 1 is in the form of thelog-likelihood ratio (LLR) of the a priori probability of b₁=0 or 1.

For an N_(t)×N_(r) M-QAM system as defined by Equation 3, the vector of[b₁ b₂ . . . b_(L)] bits where L=N_(t)log₂(M) is mapped into [x₁ x₂ . .. x_(Nt)] symbols and is transmitted. The LLR of bit b₁, 1=1, 2, . . .L, is: $\begin{matrix}{{{LLR}\left( b_{l} \right)} = {{\ln\frac{\Pr\left( {b_{l} = \left. 0 \middle| y \right.} \right)}{\Pr\left( {b_{l} = \left. 1 \middle| y \right.} \right)}} = {\ln\frac{\sum\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 0}{\Pr\left( x_{j} \middle| y \right)}}{\sum\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 1}{\Pr\left( x_{j} \middle| y \right)}}}}} & {{Eq}\quad 5}\end{matrix}$where j=1, . . . M^(Nt) denotes all possible transmit symbol vectors, yis the received symbol vector.

Applying Bayes' rule, LLR(b₁) can be rewritten as: $\begin{matrix}{{{LLR}\left( b_{l} \right)} = {{\ln\frac{\sum\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 0}{{\Pr\left( y \middle| x_{j} \right)}{\Pr\left( x_{j} \right)}}}{\sum\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 1}{{\Pr\left( y \middle| x_{j} \right)}{\Pr\left( x_{j} \right)}}}} = {\ln\frac{\sum\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 0}{\Pr\left( y \middle| x_{j} \right)}}{\sum\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 1}{\Pr\left( y \middle| x_{j} \right)}}}}} & {{Eq}\quad 6}\end{matrix}$where the last simplification is based on the assumption that x_(j)'sare equi-probable.

Given the channel matrix H, $\begin{matrix}{{{LLR}\left( b_{l} \right)} = {\ln\frac{\sum\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 0}{\mathbb{e}}^{({- \frac{{{y - {Hx}_{j}}}^{2}}{\sigma^{2}}})}}{\sum\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 1}{\mathbb{e}}^{({- \frac{{{y - {Hx}_{j}}}^{2}}{\sigma^{2}}})}}}} & {{Eq}\quad 7}\end{matrix}$Next, applying the standard max-log approximation, Eq 6 can be furthersimplified by keeping only the largest term in the summation in both thenumerator and denominator, $\begin{matrix}{{{L\overset{\bigwedge}{L}{R\left( b_{l} \right)}} = {\frac{1}{\sigma^{2}}\left( {{\min\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 1}{{y - {Hx}_{j}}}^{2}} - {\min\limits_{{\forall{x_{j}{s.t.b_{l}}}} = 0}{{y - {Hx}_{j}}}^{2}}} \right)}},} & {{Eq}\quad 8}\end{matrix}$

In a 2×2 4-QAM system, the transmitted symbols x₁, x₂ in Equation 1 areeach drawn from a 4-QAM constellation as shown in FIG. 4.

Table 1 lists all the 16 combinations of transmit symbol vectors [x₁x₂]. TABLE 1 j x_(j) = x₁ x₂ b₁b₂b₃b₄ 1 C1C1 0000 2 C1C2 0001 3 C1C30010 4 C1C4 0011 5 C2C1 0100 6 C2C2 0101 7 C2C3 0110 8 C2C4 0111 9 C3C11000 10 C3C2 1001 11 C3C3 1010 12 C3C4 1011 13 C4C1 1100 14 C4C2 1101 15C4C3 1110 16 C4C4 1111C1 = −1 − jC2 = −1 + jC3 = 1 − jC4 = 1 + j

From Equation 8, the approximate LLRs of b₁, b₂, b₃ and b₄ can becomputed as follows: $\begin{matrix}{{L\overset{\bigwedge}{L}{R\left( b_{l} \right)}} = {\frac{1}{\sigma^{2}}\left( {{\min\limits_{{\forall x_{j}},{j = 9}\quad,\ldots\quad,16}{{y - {Hx}_{j}}}^{2}} - {\min\limits_{{\forall x_{j}},{j = 1},{\ldots\quad 8}}{{y - {Hx}_{j}}}^{2}}} \right)}} & {{Eq}\quad 9} \\{{L\overset{\bigwedge}{L}{R\left( b_{2} \right)}} = {\frac{1}{\sigma^{2}}\left( {{\underset{13,\ldots\quad,16}{\min\limits_{{\forall x_{j}},{j = 5}\quad,\ldots\quad,8}}{{y - {Hx}_{j}}}^{2}} - {\underset{9,\ldots\quad,12}{\min\limits_{{\forall x_{j}},{j = 1},{\ldots\quad 4}}}{{y - {Hx}_{j}}}^{2}}} \right)}} & {{Eq}\quad 10} \\{{L\overset{\bigwedge}{L}{R\left( b_{3} \right)}} = {\frac{1}{\sigma^{2}}\left( {{\underset{11,12,15,16}{\min\limits_{{\forall x_{j}},{j = 3},4,7,8}}{{y - {Hx}_{j}}}^{2}} - {\underset{9,10,13,14}{\min\limits_{{\forall x_{j}},{j = 1},2,5,6}}{{y - {Hx}_{j}}}^{2}}} \right)}} & {{Eq}\quad 11} \\{{L\overset{\bigwedge}{L}{R\left( b_{l} \right)}} = {\frac{1}{\sigma^{2}}\left( {{\min\limits_{{\forall x_{j}},{j = {even}}}{{y - {Hx}_{j}}}^{2}} - {\min\limits_{{\forall x_{j}},{j = {odd}}}{{y - {Hx}_{j}}}^{2}}} \right)}} & {{Eq}\quad 12}\end{matrix}$

As will be understood by those of skill in the art, the ML detector isoptimal and is able to fully exploit the available diversity inherent inthe channel matrix H. Thus the ML detector can realize substantialimprovements over suboptimal equalization-based detection methods. Thedisadvantage of the ML detector, however, is that it requires anexhaustive search to find the LLRs of each bit. Moreover, thecomputational complexity of the ML detector grows exponentially withN_(t), the number of transmitter antennas.

In the method and apparatus of the present invention, an initialestimate of the transmitted symbols is be obtained, and is used toreduce the search set to N (N<M) symbols that are closest by somecriteria to the estimated transmitted symbols. Various embodiments ofthe present invention use optimizing criteria for determining thereduced search set in the present invention, as described hereinbelow.

In one embodiment of the present invention the optimizing criteriacomprises linear equalization as defined by the following equation:{circumflex over (x)}=Q(Wy)  Eq 13where W is the linear equalization matrix and Q(.) denotes the slicingoperation according to the constellation used. In an embodiment of theinvention, the linear equalization matrix is defined by a Zero-forcing(ZF) equalizer:W=(H ^(H) H)⁻¹ H ^(H)  Eq 14which is the pseudo-inverse of H. In this equation, it is assumed thatN₁>N_(t). In another embodiment of the invention, the equalizationmatrix is defined by a Minimum-mean-squared-error (MMSE) equalizer:$\begin{matrix}{W = {\left( {{H^{H}H} + {\frac{1}{SNR}I}} \right)^{- 1}H^{H}}} & {{Eq}\quad 15}\end{matrix}$

In alternative embodiment of the invention, the optimizing criteriacomprises nulling and canceling. As opposed to linear equalization whereall components of {circumflex over (x)} are estimated jointly, thenulling and canceling approach estimates the components of {circumflexover (x)} sequentially. For example, if {circumflex over (x)}₁ is firstestimated using either the ZF or MMSE linear equalization approach, thenits contribution to the received vector y is subtracted from y. Themodified received vector y is then used for estimating the nexttransmitted symbol. The whole process is repeated until all componentsof {circumflex over (x)} have been estimated.

The criteria for reducing the search set can be understood from thefollowing discussion in conjunction with the illustrations shown inFIGS. 5-8. For discussion purposes, let Ni be the number of symbolsclosest by some criteria to the estimated transmit symbol {circumflexover (x)}₁. A first criterion (hereinafter criterion 1) can be stated asfollows:

Criterion 1—If bit b_(k) belongs to {circumflex over (x)}_(m), then foreach b_(k)=0 or 1, find among all constellation points that are encodedwith b_(k)=0 or 1, the N_(m) constellation points that are closest inEuclidean distance to {circumflex over (x)}_(m). For the other transmitsymbols, {circumflex over (x)}_(i,i≠m), N_(i) is simply the N_(i)constellation points that are closest in Euclidean distance to{circumflex over (x)}_(i).

In a 2×2 4-QAM system, the received vector y is equalized to producenoisy estimates Wy. The noisy estimates Wy are then sliced to thenearest constellation points {circumflex over (x)}₁ and {circumflex over(x)}₂. These estimated transmit symbols are illustrated in FIG. 5.

Furthermore, if N₁ and N₂ are “2”: TABLE 2 Search Search Candidatetransmit symbol set for {circumflex over (X)}₁ set for {circumflex over(X)}₂ vectors b₁ = 0 C1, C2 C4, C2 {C1C4, C1C2, C2C4, C2C2} b₁ = 1 C3,C4 C4, C2 {C3C4, C3C2, C4C4, C4C2} b₂ = 0 C3, C1 C4, C2 {C3C4, C3C2,C1C4, C1C2} b₂ = 1 C4, C2 C4, C2 {C4C4, C4C2, C2C4, C2C2} b₃ = 0 C1, C3C2, C1 {C1C2, C1C1, C3C2, C3C1} b₃ = 1 C1, C3 C4, C3 {C1C4, C1C3, C3C4,C3C3} b₄ = 0 C1, C3 C2, C1 {C1C2, C1C1, C3C3, C3C1} b₄ = 1 C1, C3 C4, C3{C1C4, C1C3, C3C4, C3C3}For each b_(k)=0 or 1, the number of candidate transmit symbol vectorshas been reduced to 4 from 8 in this embodiment.

The following are the possible approaches for Criterion 2:

(1) Find the Ni closest (in Euclidean distance) constellation points toeach estimated transmit symbol {circumflex over (x)}_(i);

(2) Search over this reduced set for the transmit symbol vector thatminimizes ∥y-Hx∥². This transmit symbol vector is denoted asx_(c)=[x_(c,1) x_(c,2)];

(3) x_(c)=[x_(c,1) x_(c,2)] is the candidate transmit symbol vector forthe corresponding bits that are mapped into x_(c); and

(4) For the bit values that are not part of x_(c), there are severalways to compute the approximate LLRs, discussed in greater detailhereinbelow.

FIG. 6 is an illustration of a 2×2 16-QAM example, processed using themethod described herein where z denotes the initial estimate.{circumflex over (x)}=Q(z) is z sliced to the nearest constellationpoints. Furthermore, N₁ and N₂ are 4. Hence, the 4 closest constellationpoints to {circumflex over (x)}₁ and {circumflex over (x)}₂ arecontained in the rectangular grids. Together, they make up a reducedsearch set of 16 possible transmit symbol vectors out of which x_(c) isassumed to minimize ∥y-Hx∥². The bit representation of x_(c) is[11110001].

From the discussion above with regard to FIG. 6, it can be seen that,x_(c) minimizes ∥y-Hx∥² in the reduced search set. Bit-wise, ∥y-Hx_(c)∥²is the minimum metric for b₁=1, b₂=1, b₃=1, b₄=1, b₅=0, b₆=0, b₇=0 andb₈=1. To complete the LLR computation of each bit in Equation 8, theminimum metric must be approximated for b₁=0, b₂=0, b₃=0, b₄=0, b₅=1,b₆=1, b₇=1 and b₈=0. This is step 4 of criterion 2.

Step 4 of criterion 2 involves different methods to derive the metricsof the missing bit values in order to complete the LLR calculation ofeach bit. If b1=0 is not part of the bit representation of xc, themetric for b1=0 can be computed in a number of different ways:

(1) Method 1—search over all possible transmit symbol vectors;

(2) Method 2—slice the element of x_(c) that contains bit b₁ to theclosest P symbols with b₁=0. For the other elements of x_(c) that do notcontain bit b₁, find the Q closest symbols to these elements of x_(c).These P and Q symbols make up the reduced set of possible transmitsymbol vectors;

(3) Method 3—slice the element of xc that contains bit b₁ to the closestP symbols that share the same I-level or Q-level with b₁=0. For theother elements of x_(c) that do not contain bit b₁, find the Q closestsymbols to these elements of x_(c). These P and Q symbols make up thereduced set of possible transmit symbol vectors; or

(4) Method 4—set the metric to some fixed value that is pre-determinedto be sufficiently high. All of the above applies for the case whereb₁=1 is not part of the but representation of x_(c).

FIG. 7 and the following discussion illustrates how to derive the metricfor b₁=0 using Method 2 of Step 4 (Method 1 calls for searching ALLpossible transmit symbol vectors and hence doesn't require anyillustration). Let P and Q be 4.

Since b₁ belongs to x_(c,1), we slice x_(c,1) to the 4 closest symbols(denoted as ‘+’) with b₁=0. Since x_(c,2) does not have bit b₁, wesimply search for the 4 closest symbols to x_(c,2) (circled andincluding x_(c,2)). Out of these 16 possible transmit symbol vectors(made up of the ‘+’ and circled symbols), we can then compute the metricfor b₁=0. The same process is repeated for the metric computation ofb₂=0, b₃=0, b₄=0, b₅=1, b₅=1, b₆=1, b₇=1 and b₈=0.

FIG. 8 and the following discussion illustrate how to compute the metricfor b₁=0 using Method 3. Again, P and Q will be 4. Both the −1 and −3I-levels have b₁=0. Since b₁ belongs to x_(c,1), we slice x_(c,1) to the4 symbols on the closest I-level, which is the −1 I-level (denoted as‘+’). Since x_(c,2) doesn't have bit b₁, we simply search for the 4closest symbols to x_(c,2) (circled and including x_(c,2)). Out of these16 possible transmit symbol vectors (made up of ‘+’ and circledsymbols), we can then compute the metric for b₁=0. The same process isrepeated for the metric computation of b₂=0, b₃=0, b₄=0, b₅=1, b₅=1,b₆=1, b₇=1 and b₈=0.

As can be seen from the foregoing discussion, the method and apparatusof the present invention provides a reduced-complexitymaximum-likelihood detector that provides a high degree of signaldetection accuracy while maintaining high processing speeds. Those ofskill in the art will appreciate that the teachings of the presentinvention can be modified by using different schemes to estimate thetransmit symbols and to find the search set around the estimatedtransmit symbols. The invention can be applied to any communicationsystem with multiple transmit streams.

Although the present invention has been described in detail, it shouldbe understood that various changes, substitutions and alterations can bemade hereto without departing from the spirit and scope of the inventionas defined by the appended claims. invention as defined by the appendedclaims.

1. A communication system comprising: a plurality of transmit sourcesoperable to transmit a plurality of symbols over a plurality ofchannels; a detector operable to: receive symbols corresponding to saidtransmitted symbols; process said received symbols to obtain initialestimates of said transmitted symbols; use said initial estimates togenerate a plurality of reduced search sets; and use said reduced searchset to generate decisions for detecting said transmitted symbols.
 2. Thecommunication system of claim 1, wherein said decisions for detectingsaid transmitted symbol comprise soft decisions based on said reducedsearch set.
 3. The communication system of claim 1, wherein saiddecisions for detecting said transmitted symbol comprise a hard decisionbased on said reduced search set.
 4. The communication system of claim1, wherein said initial estimate is obtained by linear equalization ofsaid received symbols.
 5. The communication system of claim 4, whereinsaid linear equalization is obtained by using a zero-forcing equalizer.6. The communication system of claim 4, wherein said linear equalizationis obtained by using a minimum-mean-squared-error equalizer.
 7. Thecommunication system of claim 1, wherein said initial estimate isobtained by nulling and canceling of data corresponding to said receivedsymbols.
 8. The communication system of claim 1, wherein said reducedsearch set is obtained by a equalizing a vector of received symbols toobtain noisy estimates thereof and slicing said noisy estimates to a setof eligible constellation points.
 9. The communication system of claim8, wherein said noisy estimate is correlated with a candidatetransmitted symbol to generate a data output corresponding to saidtransmitted symbol.
 10. The communication system of claim 9, whereinsaid data output corresponding to said transmitted symbol is generatedusing a log-likelihood probability ratio.
 11. The communication systemof claim 1, wherein said reduced search set is obtained by: (a) findingthe eligible constellation points corresponding to each noisy estimatedtransmit symbol, thereby defining a reduced search set for thetransmitted symbol vector; and (b) searching over the reduced set forthe transmit symbol vector that minimizes ∥y-Hx∥², thereby generatingdecisions for detecting said transmitted symbols.
 12. The communicationsystem of claim 11, wherein said noisy estimate is correlated with acandidate transmitted symbol to generate a data output corresponding tosaid transmitted symbol.
 13. The communication system of claim 12,wherein said data output corresponding to said transmitted symbol isgenerated using a log-likelihood probability ratio.
 14. A method ofcommunicating data comprising: transmitting a plurality of symbols froma plurality of transmit sources over a plurality of channels; receivingsymbols corresponding to said transmitted symbols; processing saidreceived symbols to obtain initial estimates of said transmittedsymbols; using said initial estimates to generate a plurality of reducedsearch sets; and using said reduced search set to generate decisions fordetecting said transmitted symbols.
 15. The method of claim 14, whereinsaid decisions for detecting said transmitted symbol comprise softdecisions based on said reduced search set.
 16. The method of claim 14,wherein said decisions for detecting said transmitted symbol comprise ahard decision based on said reduced search set.
 17. The method of claim14, wherein said initial estimate is obtained by linear equalization ofsaid received symbols.
 18. The method of claim 17, wherein said linearequalization is obtained by using a zero-forcing equalizer.
 19. Themethod of claim 17, wherein said linear equalization is obtained byusing a minimum-mean-squared-error equalizer.
 20. The method of claim14, wherein said initial estimate is obtained by nulling and cancelingof data corresponding to said received symbols.
 21. The method of claim14, wherein said reduced search set is obtained by a equalizing a vectorof received symbols to obtain noisy estimates thereof and slicing saidnoisy estimates to a set of eligible constellation points.
 22. Themethod of claim 21, wherein said noisy estimate is correlated with acandidate transmitted symbol to generate a data output corresponding tosaid transmitted symbol.
 23. The method of claim 22, wherein said dataoutput corresponding to said transmitted symbol is generated using alog-likelihood probability ratio.
 24. The method of claim 14, whereinsaid reduced search set is obtained by: (a) finding the eligibleconstellation points corresponding to each noisy estimated transmitsymbol, thereby defining a reduced search set for the transmitted symbolvector; and (b) searching over the reduced set for the transmit symbolvector that minimizes ∥y-Hx∥², thereby decisions for detecting saidtransmitted symbols.
 25. The method of claim 24, wherein said noisyestimate is correlated with a candidate transmitted symbol to generate adata output corresponding to said transmitted symbol.
 26. The method ofclaim 25, wherein said data output corresponding to said transmittedsymbol is generated using a log-likelihood probability ratio.